Charged fixed point in the Ginzburg-Landau superconductor and the role of the Ginzburg parameter κ

We present a semi-perturbative approach which yields an infrared-stable fixed point in the Ginzburg-Landau for N = 2, where N/2 is the number of complex components. The calculations are done in d = 3 dimensions and below T-c, where the renormalization group functions can be expressed directly as functions of the Ginzburg parameter K which is the ratio between the two fundamental scales of the problem, the penetration depth; and the correlation length. We find a charged fixed point for K > 1/root2, that is, in the type II regime, where Deltak equivalent to k - 1/root2 is shown to be a natural expansion parameter. This parameter controls a momentum space instability in the two-point correlation function of the order field. This instability appears at a non-zero wave-vector p(0) whose magnitude scales like similar to Ak((beta) over bar), with a critical exponent (beta) over bar= 1/2 in the one-loop approximation, a behavior known from magnetic systems with a Lifshitz point in the phase diagram. This momentum space instability is argued to be the origin of the negative eta-exponent of the order field. (C) 2002 Elsevier Science B.V. All rights reserved.